As a roadside antiwar vigil initiated by a California woman who lost a son in Iraq continued near his ranch Thursday, President Bush said that he sympathizes with her loss but added that agreeing to her demand to immediately withdraw troops "would be a mistake for the security of this country."

Speaking to reporters after meeting with members of his national security team, Bush said he has heard the voices of Cindy Sheehan and grieving family members who say the United States should leave Iraq because of the mounting death toll.

"I grieve for every death," Bush said. "It breaks my heart to think about a family weeping over the loss of a loved one. I understand the anguish that some feel about the death that takes place."

Nonetheless, Bush said, withdrawing U.S. troops from Iraq before that nation's security forces are able to cope with the ongoing insurgency "would send a terrible signal to the enemy" that the United States is weak and easily intimidated

While Bush met with Vice President Cheney, Defense Secretary Donald H. Rumsfeld and Secretary of State Condoleezza Rice to discuss the war and other foreign policy concerns, a growing clutch of protesters gathered along the muddy shoulder of the narrow, winding road leading to Bush's 1,600-acre ranch.

Sheehan, who began her vigil Saturday, has been joined by several dozen protesters from across the country, including others who have had loved ones killed in Iraq.

"The president says he feels compassion for me, but the best way to show that compassion is by meeting with me and the other mothers and families who are here," Sheehan said. "Our sons made the ultimate sacrifice and we want answers. All we're asking is that he sacrifice an hour out of his five-week vacation to talk to us, before the next mother loses her son in Iraq."

Celeste Zappala of Philadelphia said her son, Sgt. Sherwood Baker, was killed in Baghdad while looking for nonexistent weapons of mass destruction. "This war is a disaster," Zappala said. "It is a betrayal of our military. It is a betrayal of our democracy."

The protesters have strung placards along the roadside saying things such as "Who would Jesus bomb?" and "Who lied? Who died? Who paid? Who profits?" They also drove dozens of small, white wooden crosses into the ground along the road, in honor of those killed in Iraq.

Sheehan's son, Casey Sheehan, 24, a former Eagle Scout and altar boy, was killed in Baghdad on April 4, 2004, within a week of arriving in Iraq. Sheehan met Bush two months later, as part of a group of grieving military family members. She has alleged that Bush treated her callously during their private conversation, and she has demanded a second meeting to air her grievances about the war and to tell Bush about the devastation she has felt since losing her son.

After her son's death, Sheehan, 48, co-founded Gold Star Families for Peace, an organization of people who have lost loved ones in Iraq or who oppose the war.

Although she met Saturday with two top Bush aides, Sheehan has vowed to maintain her vigil -- here and, if necessary, outside the White House -- until she is granted another meeting with the president.

Sheehan's protest has created a delicate situation for the White House, which has resisted being drawn into a public battle with a woman who lost a son in Iraq. But Sheehan's protest has also divided her own family.

Her son's aunt and godmother released a statement, accusing Sheehan of promoting her agenda at the expense of her son's name.

"We don't agree with anything she's doing," said Frank Sheehan, Casey's grandfather. "As far as we're concerned, Casey was a hero and she's dragging him through the mud."

Researcher Brian Faler contributed to this report.

Among those wading through mud to place crosses near the president's Texas ranch are, from left, Texan Marie Pugh and Californians Kathleen Hernandez and Woody Hastings.